A goodness-of-fit test for marginal distribution of linear random fields with long memory

This paper addresses the problem of fitting a known distribution function to the marginal distribution of a stationary long memory moving average random field observed on increasing $$\nu $$ ν -dimensional “cubic” domains when its mean $$\mu $$ μ and scale $$\sigma $$ σ are known or unknown. Using two suitable estimators of $$\mu $$ μ and a classical estimate of $$\sigma $$ σ , a modification of the Kolmogorov–Smirnov statistic is defined based on the residual empirical process and having a Cauchy-type limit distribution, independent of $$\mu ,\sigma $$ μ , σ and the long memory parameter d. Based on this result, a simple goodness-of-fit test for the marginal distribution is constructed, which does not require the estimation of d or any other underlying nuisance parameters. The result is new even for the case of time series, i.e., when $$\nu =1$$ ν = 1 . Findings of a simulation study investigating the finite sample behavior of size and power of the proposed test is also included in this paper. Copyright Springer-Verlag Berlin Heidelberg 2016